Quark mixing, CP violation and rare decays after the top quark discovery

We review the highlights of quark mixing, particle-antiparticle mixing, CP violation and rare K- and B-decays in the Standard Model. The top quark discovery, the precise measurement of its mass, the improved knowledge of the couplings $V_{cb}$ and $V_{ub}$, and the calculations of NLO short distance QCD corrections improved considerably the predictions for various decay rates, the determination of the couplings $V_{td}$ and $V_{ts}$ and of the complex phase in the Cabibbo-Kobayashi-Maskawa matrix. After presenting the general theoretical framework for weak decays, we discuss the following topics in detail: i) the CKM matrix, its most convenient parametrizations and the unitarity triangle, ii) the CP-violating parameter ${ϵ}_K$ and $B_{d,s}^0-{\bar{B}}_{d,s}^0$ mixings, iii) the ratio ${ϵ}^{\mathrm{\prime }}\mathrm{/}ϵ$, iv) the rare K-decays $K_L\to {\pi }^0{e}^{+}{e}^{-}$, $K^{+}\to {\pi }^{+}\nu \bar{\nu }$, $K_L\to {\pi }^0\nu \bar{\nu }$ and $K_L\to {\mu }^{+}{\mu }^{-}$, v) the radiative decays $B\to X_s\gamma$and$B\to X_s l^+l^-$,vi)therareB-decays$B\to X_{s,d}\nu\bar\nu$and$B_{d,s}\to l^+l^-$, vii) CP violation in neutral and charged B-decays putting emphasis on clean determinations of the angles of the unitarity triangle, and viii) the role of electroweak penguins in B-decays. We present several future visions demonstrating very clearly the great potential of CP asymmetries in B-decays and of clean K-decays such as $K^+\to\pi^+\nu \bar\nu$and$K_L\to\pi^0\nu\bar\nu$ in the determination of the CKM parameters and in decisive testing of the Standard Model. An outlook for the coming years ends our review.